LMFDB - Embedded newform 45.12.b.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [45,12,Mod(19,45)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(45, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 12, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("45.19");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	45.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$34.5754431252$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 142x^{2} - 2144x + 28656 $ x^4 - x^3 - 142x^2 - 2144x + 28656
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$-10.8434 + 10.0894i$ of defining polynomial
Character	$\chi$	$=$	45.19
Dual form			45.12.b.b.19.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+27.1071i q^{2} +1313.20 q^{4} +(-6581.01 + 2349.13i) q^{5} +66589.5i q^{7} +91112.6i q^{8} +O(q^{10})$	\(q+27.1071i q^{2} +1313.20 q^{4} +(-6581.01 + 2349.13i) q^{5} +66589.5i q^{7} +91112.6i q^{8} +(-63678.2 - 178392. i) q^{10} +374453. q^{11} -1.12751e6i q^{13} -1.80505e6 q^{14} +219635. q^{16} +5.82894e6i q^{17} -6.03360e6 q^{19} +(-8.64220e6 + 3.08488e6i) q^{20} +1.01503e7i q^{22} +7.51593e6i q^{23} +(3.77913e7 - 3.09193e7i) q^{25} +3.05636e7 q^{26} +8.74454e7i q^{28} -4.87039e7 q^{29} -2.71596e8 q^{31} +1.92552e8i q^{32} -1.58006e8 q^{34} +(-1.56427e8 - 4.38226e8i) q^{35} +542545. i q^{37} -1.63554e8i q^{38} +(-2.14035e8 - 5.99613e8i) q^{40} -8.20963e8 q^{41} -6.03499e8i q^{43} +4.91732e8 q^{44} -2.03735e8 q^{46} +4.69204e8i q^{47} -2.45683e9 q^{49} +(8.38134e8 + 1.02441e9i) q^{50} -1.48065e9i q^{52} -3.82491e9i q^{53} +(-2.46428e9 + 8.79637e8i) q^{55} -6.06714e9 q^{56} -1.32022e9i q^{58} -2.19696e9 q^{59} -7.28175e9 q^{61} -7.36220e9i q^{62} -4.76973e9 q^{64} +(2.64866e9 + 7.42015e9i) q^{65} +2.11343e9i q^{67} +7.65458e9i q^{68} +(1.18791e10 - 4.24029e9i) q^{70} +4.86982e9 q^{71} +1.92542e10i q^{73} -1.47068e7 q^{74} -7.92334e9 q^{76} +2.49346e10i q^{77} +4.54858e10 q^{79} +(-1.44542e9 + 5.15952e8i) q^{80} -2.22540e10i q^{82} -3.61471e10i q^{83} +(-1.36929e10 - 3.83603e10i) q^{85} +1.63591e10 q^{86} +3.41174e10i q^{88} +3.43834e9 q^{89} +7.50802e10 q^{91} +9.86994e9i q^{92} -1.27188e10 q^{94} +(3.97072e10 - 1.41737e10i) q^{95} +1.57518e11i q^{97} -6.65976e10i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 72 q^{4} + 300 q^{5}+O(q^{10}) $ 4 * q - 72 * q^4 + 300 * q^5	$ 4 q - 72 q^{4} + 300 q^{5} + 91400 q^{10} + 326352 q^{11} - 1080696 q^{14} - 9834976 q^{16} + 15460880 q^{19} - 35447400 q^{20} + 159152500 q^{25} + 325970832 q^{26} - 216242520 q^{29} - 684043072 q^{31} + 265782016 q^{34} - 394292400 q^{35} - 275204000 q^{40} - 1012873368 q^{41} + 1553573664 q^{44} + 5241789688 q^{46} - 1900646372 q^{49} + 4621170000 q^{50} - 7772763600 q^{55} - 10366738080 q^{56} - 3200971440 q^{59} - 2310471352 q^{61} - 5401150592 q^{64} - 3229723200 q^{65} + 40783573800 q^{70} + 60335466912 q^{71} + 5525992944 q^{74} - 52987638240 q^{76} + 74637768320 q^{79} - 72046927200 q^{80} - 46117585600 q^{85} - 39045421128 q^{86} - 118272499560 q^{89} + 51565095648 q^{91} - 266098749224 q^{94} + 264706278000 q^{95}+O(q^{100}) $ 4 * q - 72 * q^4 + 300 * q^5 + 91400 * q^10 + 326352 * q^11 - 1080696 * q^14 - 9834976 * q^16 + 15460880 * q^19 - 35447400 * q^20 + 159152500 * q^25 + 325970832 * q^26 - 216242520 * q^29 - 684043072 * q^31 + 265782016 * q^34 - 394292400 * q^35 - 275204000 * q^40 - 1012873368 * q^41 + 1553573664 * q^44 + 5241789688 * q^46 - 1900646372 * q^49 + 4621170000 * q^50 - 7772763600 * q^55 - 10366738080 * q^56 - 3200971440 * q^59 - 2310471352 * q^61 - 5401150592 * q^64 - 3229723200 * q^65 + 40783573800 * q^70 + 60335466912 * q^71 + 5525992944 * q^74 - 52987638240 * q^76 + 74637768320 * q^79 - 72046927200 * q^80 - 46117585600 * q^85 - 39045421128 * q^86 - 118272499560 * q^89 + 51565095648 * q^91 - 266098749224 * q^94 + 264706278000 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			27.1071i			0.598989i	0.954098	+	0.299495i	$0.0968180\pi$
$2$			27.1071i			0.598989i	−0.954098	+	0.299495i	$0.903182\pi$
$3$		0			0
$3$		0			0
$4$	1313.20			0.641212
$5$	−6581.01	+	2349.13i	−0.941798	+	0.336180i
$5$	−6581.01	+	2349.13i	−0.941798	+	0.336180i
$6$		0			0
$7$			66589.5i			1.49750i	0.662854	+	0.748749i	$0.269345\pi$
$7$			66589.5i			1.49750i	−0.662854	+	0.748749i	$0.730655\pi$
$8$			91112.6i			0.983068i
$9$		0			0
$10$	−63678.2	−	178392.i	−0.201368	−	0.564127i
$11$	374453.			0.701031			0.350515	−	0.936557i	$-0.386006\pi$
$11$	374453.			0.701031			0.350515	+	0.936557i	$0.386006\pi$
$12$		0			0
$13$		−	1.12751e6i		−	0.842232i	−0.907007	−	0.421116i	$-0.861639\pi$
$13$		−	1.12751e6i		−	0.842232i	0.907007	−	0.421116i	$-0.138361\pi$
$14$	−1.80505e6			−0.896985
$15$		0			0
$16$	219635.			0.0523651
$17$			5.82894e6i			0.995681i	0.867269	+	0.497841i	$0.165874\pi$
$17$			5.82894e6i			0.995681i	−0.867269	+	0.497841i	$0.834126\pi$
$18$		0			0
$19$	−6.03360e6			−0.559026			−0.279513	−	0.960142i	$-0.590173\pi$
$19$	−6.03360e6			−0.559026			−0.279513	+	0.960142i	$0.590173\pi$
$20$	−8.64220e6	+	3.08488e6i	−0.603892	+	0.215563i
$21$		0			0
$22$			1.01503e7i			0.419910i
$23$			7.51593e6i			0.243489i	0.992561	+	0.121745i	$0.0388489\pi$
$23$			7.51593e6i			0.243489i	−0.992561	+	0.121745i	$0.961151\pi$
$24$		0			0
$25$	3.77913e7	−	3.09193e7i	0.773966	−	0.633227i
$26$	3.05636e7			0.504488
$27$		0			0
$28$			8.74454e7i			0.960214i
$29$	−4.87039e7			−0.440935			−0.220467	−	0.975394i	$-0.570758\pi$
$29$	−4.87039e7			−0.440935			−0.220467	+	0.975394i	$0.570758\pi$
$30$		0			0
$31$	−2.71596e8			−1.70386			−0.851932	−	0.523653i	$-0.824569\pi$
$31$	−2.71596e8			−1.70386			−0.851932	+	0.523653i	$0.824569\pi$
$32$			1.92552e8i			1.01443i
$33$		0			0
$34$	−1.58006e8			−0.596402
$35$	−1.56427e8	−	4.38226e8i	−0.503429	−	1.41034i
$36$		0			0
$37$			542545.i			0.00128625i	1.00000		0.000643126i	$0.000204713\pi$
$37$			542545.i			0.00128625i	−1.00000		0.000643126i	$0.999795\pi$
$38$		−	1.63554e8i		−	0.334850i
$39$		0			0
$40$	−2.14035e8	−	5.99613e8i	−0.330488	−	0.925851i
$41$	−8.20963e8			−1.10666			−0.553328	−	0.832964i	$-0.686642\pi$
$41$	−8.20963e8			−1.10666			−0.553328	+	0.832964i	$0.686642\pi$
$42$		0			0
$43$		−	6.03499e8i		−	0.626037i	−0.949747	−	0.313018i	$-0.898660\pi$
$43$		−	6.03499e8i		−	0.626037i	0.949747	−	0.313018i	$-0.101340\pi$
$44$	4.91732e8			0.449509
$45$		0			0
$46$	−2.03735e8			−0.145847
$47$			4.69204e8i			0.298417i	0.988806	+	0.149208i	$0.0476725\pi$
$47$			4.69204e8i			0.298417i	−0.988806	+	0.149208i	$0.952327\pi$
$48$		0			0
$49$	−2.45683e9			−1.24250
$50$	8.38134e8	+	1.02441e9i	0.379296	+	0.463597i
$51$		0			0
$52$		−	1.48065e9i		−	0.540049i
$53$		−	3.82491e9i		−	1.25633i	−0.778079	−	0.628166i	$-0.783806\pi$
$53$		−	3.82491e9i		−	1.25633i	0.778079	−	0.628166i	$-0.216194\pi$
$54$		0			0
$55$	−2.46428e9	+	8.79637e8i	−0.660229	+	0.235672i
$56$	−6.06714e9			−1.47214
$57$		0			0
$58$		−	1.32022e9i		−	0.264115i
$59$	−2.19696e9			−0.400069			−0.200035	−	0.979789i	$-0.564105\pi$
$59$	−2.19696e9			−0.400069			−0.200035	+	0.979789i	$0.564105\pi$
$60$		0			0
$61$	−7.28175e9			−1.10388			−0.551940	−	0.833884i	$-0.686112\pi$
$61$	−7.28175e9			−1.10388			−0.551940	+	0.833884i	$0.686112\pi$
$62$		−	7.36220e9i		−	1.02060i
$63$		0			0
$64$	−4.76973e9			−0.555270
$65$	2.64866e9	+	7.42015e9i	0.283141	+	0.793212i
$66$		0			0
$67$			2.11343e9i			0.191239i	0.995418	+	0.0956197i	$0.0304833\pi$
$67$			2.11343e9i			0.191239i	−0.995418	+	0.0956197i	$0.969517\pi$
$68$			7.65458e9i			0.638443i
$69$		0			0
$70$	1.18791e10	−	4.24029e9i	0.844778	−	0.301548i
$71$	4.86982e9			0.320326			0.160163	−	0.987091i	$-0.448798\pi$
$71$	4.86982e9			0.320326			0.160163	+	0.987091i	$0.448798\pi$
$72$		0			0
$73$			1.92542e10i			1.08705i	0.839393	+	0.543524i	$0.182910\pi$
$73$			1.92542e10i			1.08705i	−0.839393	+	0.543524i	$0.817090\pi$
$74$	−1.47068e7			−0.000770451
$75$		0			0
$76$	−7.92334e9			−0.358454
$77$			2.49346e10i			1.04979i
$78$		0			0
$79$	4.54858e10			1.66313			0.831566	−	0.555426i	$-0.187445\pi$
$79$	4.54858e10			1.66313			0.831566	+	0.555426i	$0.187445\pi$
$80$	−1.44542e9	+	5.15952e8i	−0.0493174	+	0.0176041i
$81$		0			0
$82$		−	2.22540e10i		−	0.662874i
$83$		−	3.61471e10i		−	1.00726i	−0.863918	−	0.503632i	$-0.831997\pi$
$83$		−	3.61471e10i		−	1.00726i	0.863918	−	0.503632i	$-0.168003\pi$
$84$		0			0
$85$	−1.36929e10	−	3.83603e10i	−0.334728	−	0.937730i
$86$	1.63591e10			0.374989
$87$		0			0
$88$			3.41174e10i			0.689161i
$89$	3.43834e9			0.0652685			0.0326342	−	0.999467i	$-0.489610\pi$
$89$	3.43834e9			0.0652685			0.0326342	+	0.999467i	$0.489610\pi$
$90$		0			0
$91$	7.50802e10			1.26124
$92$			9.86994e9i			0.156128i
$93$		0			0
$94$	−1.27188e10			−0.178748
$95$	3.97072e10	−	1.41737e10i	0.526489	−	0.187933i
$96$		0			0
$97$			1.57518e11i			1.86246i	0.364436	+	0.931228i	$0.381262\pi$
$97$			1.57518e11i			1.86246i	−0.364436	+	0.931228i	$0.618738\pi$
$98$		−	6.65976e10i		−	0.744244i
$99$		0			0
$100$	4.96277e10	−	4.06033e10i	0.496277	−	0.406033i
$101$	3.14292e10			0.297554			0.148777	−	0.988871i	$-0.452466\pi$
$101$	3.14292e10			0.297554			0.148777	+	0.988871i	$0.452466\pi$
$102$		0			0
$103$		−	3.42578e10i		−	0.291176i	−0.989345	−	0.145588i	$-0.953493\pi$
$103$		−	3.42578e10i		−	0.291176i	0.989345	−	0.145588i	$-0.0465074\pi$
$104$	1.02730e11			0.827971
$105$		0			0
$106$	1.03683e11			0.752529
$107$			2.10883e11i			1.45355i	0.686874	+	0.726776i	$0.258982\pi$
$107$			2.10883e11i			1.45355i	−0.686874	+	0.726776i	$0.741018\pi$
$108$		0			0
$109$	−1.44958e10			−0.0902394			−0.0451197	−	0.998982i	$-0.514367\pi$
$109$	−1.44958e10			−0.0902394			−0.0451197	+	0.998982i	$0.514367\pi$
$110$	−2.38444e10	−	6.67995e10i	−0.141165	−	0.395470i
$111$		0			0
$112$			1.46254e10i			0.0784167i
$113$		−	2.14619e9i		−	0.0109581i	−0.999985	−	0.00547906i	$-0.998256\pi$
$113$		−	2.14619e9i		−	0.0109581i	0.999985	−	0.00547906i	$-0.00174405\pi$
$114$		0			0
$115$	−1.76559e10	−	4.94624e10i	−0.0818562	−	0.229318i
$116$	−6.39580e10			−0.282733
$117$		0			0
$118$		−	5.95532e10i		−	0.239637i
$119$	−3.88146e11			−1.49103
$120$		0			0
$121$	−1.45097e11			−0.508556
$122$		−	1.97388e11i		−	0.661212i
$123$		0			0
$124$	−3.56661e11			−1.09254
$125$	−1.76072e11	+	2.92257e11i	−0.516042	+	0.856563i
$126$		0			0
$127$		−	2.28294e8i		−	0.000613160i	−1.00000		0.000306580i	$-0.999902\pi$
$127$		−	2.28294e8i		−	0.000613160i	1.00000		0.000306580i	$-9.75875e-5\pi$
$128$			2.65053e11i			0.681834i
$129$		0			0
$130$	−2.01139e11	+	7.17977e10i	−0.475125	+	0.169599i
$131$	5.23011e11			1.18446			0.592228	−	0.805771i	$-0.298249\pi$
$131$	5.23011e11			1.18446			0.592228	+	0.805771i	$0.298249\pi$
$132$		0			0
$133$		−	4.01774e11i		−	0.837140i
$134$	−5.72892e10			−0.114550
$135$		0			0
$136$	−5.31090e11			−0.978822
$137$		−	2.04327e11i		−	0.361712i	−0.983510	−	0.180856i	$-0.942113\pi$
$137$		−	2.04327e11i		−	0.361712i	0.983510	−	0.180856i	$-0.0578868\pi$
$138$		0			0
$139$	1.10282e11			0.180270			0.0901348	−	0.995930i	$-0.471270\pi$
$139$	1.10282e11			0.180270			0.0901348	+	0.995930i	$0.471270\pi$
$140$	−2.05421e11	−	5.75480e11i	−0.322805	−	0.904327i
$141$		0			0
$142$			1.32007e11i			0.191872i
$143$		−	4.22199e11i		−	0.590430i
$144$		0			0
$145$	3.20521e11	−	1.14412e11i	0.415272	−	0.148233i
$146$	−5.21926e11			−0.651130
$147$		0			0
$148$			7.12471e8i			0.000824761i
$149$	−5.11067e11			−0.570102			−0.285051	−	0.958512i	$-0.592011\pi$
$149$	−5.11067e11			−0.570102			−0.285051	+	0.958512i	$0.592011\pi$
$150$		0			0
$151$	−3.26638e10			−0.0338605			−0.0169303	−	0.999857i	$-0.505389\pi$
$151$	−3.26638e10			−0.0338605			−0.0169303	+	0.999857i	$0.505389\pi$
$152$		−	5.49737e11i		−	0.549560i
$153$		0			0
$154$	−6.75906e11			−0.628814
$155$	1.78738e12	−	6.38015e11i	1.60469	−	0.572804i
$156$		0			0
$157$			1.29615e12i			1.08444i	0.840236	+	0.542221i	$0.182416\pi$
$157$			1.29615e12i			1.08444i	−0.840236	+	0.542221i	$0.817584\pi$
$158$			1.23299e12i			0.996198i
$159$		0			0
$160$	−4.52330e11	−	1.26719e12i	−0.341032	−	0.955392i
$161$	−5.00482e11			−0.364625
$162$		0			0
$163$		−	9.53484e11i		−	0.649055i	−0.945876	−	0.324527i	$-0.894795\pi$
$163$		−	9.53484e11i		−	0.649055i	0.945876	−	0.324527i	$-0.105205\pi$
$164$	−1.07809e12			−0.709601
$165$		0			0
$166$	9.79844e11			0.603340
$167$			2.16450e12i			1.28949i	0.764398	+	0.644745i	$0.223036\pi$
$167$			2.16450e12i			1.28949i	−0.764398	+	0.644745i	$0.776964\pi$
$168$		0			0
$169$	5.20883e11			0.290645
$170$	1.03984e12	−	3.71176e11i	0.561690	−	0.200498i
$171$		0			0
$172$		−	7.92516e11i		−	0.401422i
$173$		−	3.76047e11i		−	0.184497i	−0.995736	−	0.0922483i	$-0.970595\pi$
$173$		−	3.76047e11i		−	0.184497i	0.995736	−	0.0922483i	$-0.0294054\pi$
$174$		0			0
$175$	2.05890e12	+	2.51650e12i	0.948256	+	1.15901i
$176$	8.22430e10			0.0367096
$177$		0			0
$178$			9.32035e10i			0.0390951i
$179$	9.97885e11			0.405872			0.202936	−	0.979192i	$-0.434952\pi$
$179$	9.97885e11			0.405872			0.202936	+	0.979192i	$0.434952\pi$
$180$		0			0
$181$	3.32751e12			1.27317			0.636587	−	0.771205i	$-0.280346\pi$
$181$	3.32751e12			1.27317			0.636587	+	0.771205i	$0.280346\pi$
$182$			2.03521e12i			0.755469i
$183$		0			0
$184$	−6.84796e11			−0.239366
$185$	−1.27451e9	−	3.57049e9i	−0.000432412	−	0.00121139i
$186$		0			0
$187$			2.18266e12i			0.698003i
$188$			6.16160e11i			0.191348i
$189$		0			0
$190$	3.84209e11	+	1.07635e12i	0.112570	+	0.315361i
$191$	4.02856e12			1.14674			0.573372	−	0.819295i	$-0.305635\pi$
$191$	4.02856e12			1.14674			0.573372	+	0.819295i	$0.305635\pi$
$192$		0			0
$193$			1.01858e12i			0.273798i	0.990585	+	0.136899i	$0.0437135\pi$
$193$			1.01858e12i			0.273798i	−0.990585	+	0.136899i	$0.956286\pi$
$194$	−4.26987e12			−1.11559
$195$		0			0
$196$	−3.22631e12			−0.796706
$197$		−	4.56750e12i		−	1.09677i	−0.836227	−	0.548384i	$-0.815243\pi$
$197$		−	4.56750e12i		−	1.09677i	0.836227	−	0.548384i	$-0.184757\pi$
$198$		0			0
$199$	2.19872e12			0.499435			0.249717	−	0.968319i	$-0.419662\pi$
$199$	2.19872e12			0.499435			0.249717	+	0.968319i	$0.419662\pi$
$200$	2.81714e12	+	3.44327e12i	0.622505	+	0.760862i
$201$		0			0
$202$			8.51955e11i			0.178231i
$203$		−	3.24316e12i		−	0.660299i
$204$		0			0
$205$	5.40277e12	−	1.92855e12i	1.04225	−	0.372035i
$206$	9.28632e11			0.174411
$207$		0			0
$208$		−	2.47641e11i		−	0.0441036i
$209$	−2.25930e12			−0.391894
$210$		0			0
$211$	8.39469e11			0.138182			0.0690910	−	0.997610i	$-0.477990\pi$
$211$	8.39469e11			0.138182			0.0690910	+	0.997610i	$0.477990\pi$
$212$		−	5.02289e12i		−	0.805575i
$213$		0			0
$214$	−5.71644e12			−0.870662
$215$	1.41770e12	+	3.97163e12i	0.210461	+	0.589600i
$216$		0			0
$217$		−	1.80855e13i		−	2.55153i
$218$		−	3.92940e11i		−	0.0540524i
$219$		0			0
$220$	−3.23609e12	+	1.15514e12i	−0.423347	+	0.151116i
$221$	6.57218e12			0.838595
$222$		0			0
$223$			1.61958e13i			1.96665i	0.181867	+	0.983323i	$0.441786\pi$
$223$			1.61958e13i			1.96665i	−0.181867	+	0.983323i	$0.558214\pi$
$224$	−1.28220e13			−1.51911
$225$		0			0
$226$	5.81770e10			0.00656379
$227$		−	6.08481e11i		−	0.0670046i	−0.999439	−	0.0335023i	$-0.989334\pi$
$227$		−	6.08481e11i		−	0.0670046i	0.999439	−	0.0335023i	$-0.0106661\pi$
$228$		0			0
$229$	−1.59740e13			−1.67617			−0.838083	−	0.545542i	$-0.816324\pi$
$229$	−1.59740e13			−1.67617			−0.838083	+	0.545542i	$0.816324\pi$
$230$	1.34079e12	−	4.78601e11i	0.137359	−	0.0490309i
$231$		0			0
$232$		−	4.43754e12i		−	0.433469i
$233$			1.09497e13i			1.04459i	0.852764	+	0.522296i	$0.174924\pi$
$233$			1.09497e13i			1.04459i	−0.852764	+	0.522296i	$0.825076\pi$
$234$		0			0
$235$	−1.10222e12	−	3.08784e12i	−0.100322	−	0.281048i
$236$	−2.88505e12			−0.256529
$237$		0			0
$238$		−	1.05215e13i		−	0.893111i
$239$	−2.11532e13			−1.75464			−0.877321	−	0.479905i	$-0.840671\pi$
$239$	−2.11532e13			−1.75464			−0.877321	+	0.479905i	$0.840671\pi$
$240$		0			0
$241$	1.41468e13			1.12089			0.560447	−	0.828190i	$-0.310629\pi$
$241$	1.41468e13			1.12089			0.560447	+	0.828190i	$0.310629\pi$
$242$		−	3.93317e12i		−	0.304619i
$243$		0			0
$244$	−9.56242e12			−0.707821
$245$	1.61684e13	−	5.77141e12i	1.17018	−	0.417704i
$246$		0			0
$247$			6.80294e12i			0.470829i
$248$		−	2.47459e13i		−	1.67501i
$249$		0			0
$250$	−7.92225e12	−	4.77280e12i	−0.513072	−	0.309103i
$251$	1.64508e12			0.104227			0.0521136	−	0.998641i	$-0.483404\pi$
$251$	1.64508e12			0.104227			0.0521136	+	0.998641i	$0.483404\pi$
$252$		0			0
$253$			2.81436e12i			0.170693i
$254$	6.18840e9			0.000367276
$255$		0			0
$256$	−1.69533e13			−0.963681
$257$			3.16010e13i			1.75820i	0.476635	+	0.879101i	$0.341856\pi$
$257$			3.16010e13i			1.75820i	−0.476635	+	0.879101i	$0.658144\pi$
$258$		0			0
$259$	−3.61278e10			−0.00192616
$260$	3.47823e12	+	9.74416e12i	0.181554	+	0.508617i
$261$		0			0
$262$			1.41773e13i			0.709476i
$263$			1.50443e12i			0.0737250i	0.999320	+	0.0368625i	$0.0117364\pi$
$263$			1.50443e12i			0.0737250i	−0.999320	+	0.0368625i	$0.988264\pi$
$264$		0			0
$265$	8.98521e12	+	2.51718e13i	0.422353	+	1.18321i
$266$	1.08910e13			0.501438
$267$		0			0
$268$			2.77537e12i			0.122625i
$269$	−3.90666e13			−1.69110			−0.845548	−	0.533900i	$-0.820726\pi$
$269$	−3.90666e13			−1.69110			−0.845548	+	0.533900i	$0.820726\pi$
$270$		0			0
$271$	−4.54729e12			−0.188982			−0.0944912	−	0.995526i	$-0.530122\pi$
$271$	−4.54729e12			−0.188982			−0.0944912	+	0.995526i	$0.530122\pi$
$272$			1.28024e12i			0.0521390i
$273$		0			0
$274$	5.53873e12			0.216662
$275$	1.41511e13	−	1.15778e13i	0.542574	−	0.443911i
$276$		0			0
$277$		−	2.22049e13i		−	0.818105i	−0.912511	−	0.409053i	$-0.865859\pi$
$277$		−	2.22049e13i		−	0.818105i	0.912511	−	0.409053i	$-0.134141\pi$
$278$			2.98943e12i			0.107980i
$279$		0			0
$280$	3.99279e13	−	1.42525e13i	1.38646	−	0.494905i
$281$	2.26709e13			0.771941			0.385970	−	0.922511i	$-0.373867\pi$
$281$	2.26709e13			0.771941			0.385970	+	0.922511i	$0.373867\pi$
$282$		0			0
$283$		−	2.94259e13i		−	0.963617i	−0.876276	−	0.481809i	$-0.839980\pi$
$283$		−	2.94259e13i		−	0.963617i	0.876276	−	0.481809i	$-0.160020\pi$
$284$	6.39505e12			0.205397
$285$		0			0
$286$	1.14446e13			0.353661
$287$		−	5.46675e13i		−	1.65721i
$288$		0			0
$289$	2.95383e11			0.00861880
$290$	3.10137e12	+	8.68840e12i	0.0887902	+	0.248743i
$291$		0			0
$292$			2.52846e13i			0.697029i
$293$			4.02146e13i			1.08796i	0.839099	+	0.543979i	$0.183083\pi$
$293$			4.02146e13i			1.08796i	−0.839099	+	0.543979i	$0.816917\pi$
$294$		0			0
$295$	1.44582e13	−	5.16093e12i	0.376785	−	0.134495i
$296$	−4.94327e10			−0.00126447
$297$		0			0
$298$		−	1.38536e13i		−	0.341485i
$299$	8.47428e12			0.205074
$300$		0			0
$301$	4.01866e13			0.937489
$302$		−	8.85423e11i		−	0.0202821i
$303$		0			0
$304$	−1.32519e12			−0.0292735
$305$	4.79213e13	−	1.71058e13i	1.03963	−	0.371102i
$306$		0			0
$307$			1.17567e13i			0.246050i	0.992404	+	0.123025i	$0.0392595\pi$
$307$			1.17567e13i			0.246050i	−0.992404	+	0.123025i	$0.960740\pi$
$308$			3.27442e13i			0.673139i
$309$		0			0
$310$	1.72948e13	+	4.84508e13i	0.343104	+	0.961195i
$311$	−9.66888e12			−0.188449			−0.0942245	−	0.995551i	$-0.530037\pi$
$311$	−9.66888e12			−0.188449			−0.0942245	+	0.995551i	$0.530037\pi$
$312$		0			0
$313$			7.95938e13i			1.49756i	0.662817	+	0.748782i	$0.269361\pi$
$313$			7.95938e13i			1.49756i	−0.662817	+	0.748782i	$0.730639\pi$
$314$	−3.51349e13			−0.649569
$315$		0			0
$316$	5.97321e13			1.06642
$317$			3.01135e13i			0.528366i	0.964473	+	0.264183i	$0.0851023\pi$
$317$			3.01135e13i			0.528366i	−0.964473	+	0.264183i	$0.914898\pi$
$318$		0			0
$319$	−1.82373e13			−0.309109
$320$	3.13897e13	−	1.12047e13i	0.522952	−	0.186671i
$321$		0			0
$322$		−	1.35666e13i		−	0.218406i
$323$		−	3.51695e13i		−	0.556611i
$324$		0			0
$325$	−3.48618e13	−	4.26101e13i	−0.533324	−	0.651859i
$326$	2.58462e13			0.388777
$327$		0			0
$328$		−	7.48001e13i		−	1.08792i
$329$	−3.12440e13			−0.446879
$330$		0			0
$331$	−9.09460e13			−1.25814			−0.629071	−	0.777348i	$-0.716564\pi$
$331$	−9.09460e13			−1.25814			−0.629071	+	0.777348i	$0.716564\pi$
$332$		−	4.74684e13i		−	0.645870i
$333$		0			0
$334$	−5.86735e13			−0.772390
$335$	−4.96473e12	−	1.39085e13i	−0.0642908	−	0.180109i
$336$		0			0
$337$			6.71550e13i			0.841616i	0.907150	+	0.420808i	$0.138253\pi$
$337$			6.71550e13i			0.841616i	−0.907150	+	0.420808i	$0.861747\pi$
$338$			1.41197e13i			0.174093i
$339$		0			0
$340$	−1.79816e13	−	5.03749e13i	−0.214632	−	0.601284i
$341$	−1.01700e14			−1.19446
$342$		0			0
$343$		−	3.19298e13i		−	0.363144i
$344$	5.49863e13			0.615437
$345$		0			0
$346$	1.01936e13			0.110511
$347$			1.00178e14i			1.06895i	0.845183	+	0.534476i	$0.179491\pi$
$347$			1.00178e14i			1.06895i	−0.845183	+	0.534476i	$0.820509\pi$
$348$		0			0
$349$	−3.57336e12			−0.0369434			−0.0184717	−	0.999829i	$-0.505880\pi$
$349$	−3.57336e12			−0.0369434			−0.0184717	+	0.999829i	$0.505880\pi$
$350$	−6.82152e13	+	5.58109e13i	−0.694236	+	0.567995i
$351$		0			0
$352$			7.21017e13i			0.711149i
$353$		−	4.27043e13i		−	0.414677i	−0.978269	−	0.207339i	$-0.933520\pi$
$353$		−	4.27043e13i		−	0.414677i	0.978269	−	0.207339i	$-0.0664802\pi$
$354$		0			0
$355$	−3.20483e13	+	1.14398e13i	−0.301682	+	0.107687i
$356$	4.51523e12			0.0418509
$357$		0			0
$358$			2.70498e13i			0.243113i
$359$	−1.34889e14			−1.19387			−0.596934	−	0.802290i	$-0.703615\pi$
$359$	−1.34889e14			−1.19387			−0.596934	+	0.802290i	$0.703615\pi$
$360$		0			0
$361$	−8.00859e13			−0.687490
$362$			9.01994e13i			0.762617i
$363$		0			0
$364$	9.85956e13			0.808723
$365$	−4.52305e13	−	1.26712e14i	−0.365444	−	1.02378i
$366$		0			0
$367$		−	1.04526e14i		−	0.819519i	−0.912193	−	0.409760i	$-0.865613\pi$
$367$		−	1.04526e14i		−	0.819519i	0.912193	−	0.409760i	$-0.134387\pi$
$368$			1.65076e12i			0.0127503i
$369$		0			0
$370$	9.67859e10	−	3.45483e10i	0.000725609	−	0.000259010i
$371$	2.54699e14			1.88135
$372$		0			0
$373$		−	2.42814e14i		−	1.74131i	−0.491896	−	0.870654i	$-0.663696\pi$
$373$		−	2.42814e14i		−	1.74131i	0.491896	−	0.870654i	$-0.336304\pi$
$374$	−5.91657e13			−0.418096
$375$		0			0
$376$	−4.27504e13			−0.293364
$377$			5.49141e13i			0.371369i
$378$		0			0
$379$	−1.40487e14			−0.922827			−0.461413	−	0.887185i	$-0.652657\pi$
$379$	−1.40487e14			−0.922827			−0.461413	+	0.887185i	$0.652657\pi$
$380$	5.21436e13	−	1.86129e13i	0.337591	−	0.120505i
$381$		0			0
$382$			1.09203e14i			0.686886i
$383$		−	2.17176e14i		−	1.34654i	−0.739398	−	0.673269i	$-0.764890\pi$
$383$		−	2.17176e14i		−	1.34654i	0.739398	−	0.673269i	$-0.235110\pi$
$384$		0			0
$385$	−5.85745e13	−	1.64095e14i	−0.352919	−	0.988692i
$386$	−2.76108e13			−0.164002
$387$		0			0
$388$			2.06853e14i			1.19423i
$389$	2.28055e14			1.29812			0.649062	−	0.760735i	$-0.275161\pi$
$389$	2.28055e14			1.29812			0.649062	+	0.760735i	$0.275161\pi$
$390$		0			0
$391$	−4.38099e13			−0.242438
$392$		−	2.23848e14i		−	1.22146i
$393$		0			0
$394$	1.23812e14			0.656951
$395$	−2.99343e14	+	1.06852e14i	−1.56633	+	0.559112i
$396$		0			0
$397$		−	7.68462e13i		−	0.391088i	−0.980695	−	0.195544i	$-0.937353\pi$
$397$		−	7.68462e13i		−	0.391088i	0.980695	−	0.195544i	$-0.0626473\pi$
$398$			5.96011e13i			0.299156i
$399$		0			0
$400$	8.30031e12	−	6.79097e12i	0.0405289	−	0.0331590i
$401$	−2.93708e14			−1.41456			−0.707282	−	0.706932i	$-0.750079\pi$
$401$	−2.93708e14			−1.41456			−0.707282	+	0.706932i	$0.750079\pi$
$402$		0			0
$403$			3.06228e14i			1.43505i
$404$	4.12728e13			0.190795
$405$		0			0
$406$	8.79129e13			0.395512
$407$			2.03157e11i			0.000901702i
$408$		0			0
$409$	−1.31901e14			−0.569861			−0.284930	−	0.958548i	$-0.591970\pi$
$409$	−1.31901e14			−0.569861			−0.284930	+	0.958548i	$0.591970\pi$
$410$	5.22774e13	+	1.46454e14i	0.222845	+	0.624294i
$411$		0			0
$412$		−	4.49875e13i		−	0.186705i
$413$		−	1.46294e14i		−	0.599103i
$414$		0			0
$415$	8.49141e13	+	2.37884e14i	0.338622	+	0.948639i
$416$	2.17105e14			0.854389
$417$		0			0
$418$		−	6.12431e13i		−	0.234740i
$419$	3.47913e14			1.31612			0.658058	−	0.752967i	$-0.271378\pi$
$419$	3.47913e14			1.31612			0.658058	+	0.752967i	$0.271378\pi$
$420$		0			0
$421$	3.60019e14			1.32670			0.663351	−	0.748308i	$-0.269134\pi$
$421$	3.60019e14			1.32670			0.663351	+	0.748308i	$0.269134\pi$
$422$			2.27556e13i			0.0827695i
$423$		0			0
$424$	3.48498e14			1.23506
$425$	1.80227e14	+	2.20283e14i	0.630492	+	0.770624i
$426$		0			0
$427$		−	4.84888e14i		−	1.65306i
$428$			2.76932e14i			0.932035i
$429$		0			0
$430$	−1.07660e14	+	3.84297e13i	−0.353164	+	0.126064i
$431$	−4.03045e14			−1.30535			−0.652677	−	0.757636i	$-0.726354\pi$
$431$	−4.03045e14			−1.30535			−0.652677	+	0.757636i	$0.726354\pi$
$432$		0			0
$433$			3.79440e14i			1.19801i	0.800746	+	0.599004i	$0.204437\pi$
$433$			3.79440e14i			1.19801i	−0.800746	+	0.599004i	$0.795563\pi$
$434$	4.90245e14			1.52834
$435$		0			0
$436$	−1.90359e13			−0.0578626
$437$		−	4.53481e13i		−	0.136117i
$438$		0			0
$439$	5.70014e14			1.66852			0.834259	−	0.551373i	$-0.185896\pi$
$439$	5.70014e14			1.66852			0.834259	+	0.551373i	$0.185896\pi$
$440$	−8.01460e13	−	2.24527e14i	−0.231682	−	0.649050i
$441$		0			0
$442$			1.78153e14i			0.502309i
$443$			6.54692e14i			1.82312i	0.411162	+	0.911562i	$0.365123\pi$
$443$			6.54692e14i			1.82312i	−0.411162	+	0.911562i	$0.634877\pi$
$444$		0			0
$445$	−2.26277e13	+	8.07709e12i	−0.0614697	+	0.0219419i
$446$	−4.39023e14			−1.17800
$447$		0			0
$448$		−	3.17614e14i		−	0.831515i
$449$	2.16742e14			0.560515			0.280258	−	0.959925i	$-0.409580\pi$
$449$	2.16742e14			0.560515			0.280258	+	0.959925i	$0.409580\pi$
$450$		0			0
$451$	−3.07412e14			−0.775799
$452$		−	2.81838e12i		−	0.00702648i
$453$		0			0
$454$	1.64942e13			0.0401350
$455$	−4.94104e14	+	1.76373e14i	−1.18783	+	0.424004i
$456$		0			0
$457$			4.04825e14i			0.950011i	0.879983	+	0.475006i	$0.157554\pi$
$457$			4.04825e14i			0.950011i	−0.879983	+	0.475006i	$0.842446\pi$
$458$		−	4.33008e14i		−	1.00401i
$459$		0			0
$460$	−2.31858e13	−	6.49542e13i	−0.0524872	−	0.147041i
$461$	4.78062e14			1.06937			0.534686	−	0.845051i	$-0.320430\pi$
$461$	4.78062e14			1.06937			0.534686	+	0.845051i	$0.320430\pi$
$462$		0			0
$463$			7.90859e13i			0.172744i	0.996263	+	0.0863721i	$0.0275274\pi$
$463$			7.90859e13i			0.172744i	−0.996263	+	0.0863721i	$0.972473\pi$
$464$	−1.06971e13			−0.0230896
$465$		0			0
$466$	−2.96816e14			−0.625699
$467$		−	3.83987e14i		−	0.799970i	−0.916522	−	0.399985i	$-0.869015\pi$
$467$		−	3.83987e14i		−	0.799970i	0.916522	−	0.399985i	$-0.130985\pi$
$468$		0			0
$469$	−1.40732e14			−0.286381
$470$	8.37024e13	−	2.98780e13i	0.168345	−	0.0600916i
$471$		0			0
$472$		−	2.00170e14i		−	0.393295i
$473$		−	2.25982e14i		−	0.438871i
$474$		0			0
$475$	−2.28018e14	+	1.86555e14i	−0.432667	+	0.353990i
$476$	−5.09714e14			−0.956067
$477$		0			0
$478$		−	5.73404e14i		−	1.05101i
$479$	4.33999e14			0.786400			0.393200	−	0.919453i	$-0.371368\pi$
$479$	4.33999e14			0.786400			0.393200	+	0.919453i	$0.371368\pi$
$480$		0			0
$481$	6.11724e11			0.00108332
$482$			3.83480e14i			0.671404i
$483$		0			0
$484$	−1.90542e14			−0.326092
$485$	−3.70030e14	−	1.03663e15i	−0.626120	−	1.75406i
$486$		0			0
$487$		−	3.35969e14i		−	0.555763i	−0.960615	−	0.277881i	$-0.910368\pi$
$487$		−	3.35969e14i		−	0.555763i	0.960615	−	0.277881i	$-0.0896322\pi$
$488$		−	6.63460e14i		−	1.08519i
$489$		0			0
$490$	1.56446e14	+	4.38280e14i	0.250200	+	0.700928i
$491$	6.44062e14			1.01854			0.509272	−	0.860606i	$-0.329915\pi$
$491$	6.44062e14			1.01854			0.509272	+	0.860606i	$0.329915\pi$
$492$		0			0
$493$		−	2.83892e14i		−	0.439031i
$494$	−1.84408e14			−0.282022
$495$		0			0
$496$	−5.96522e13			−0.0892231
$497$			3.24278e14i			0.479687i
$498$		0			0
$499$	6.77869e14			0.980828			0.490414	−	0.871490i	$-0.336846\pi$
$499$	6.77869e14			0.980828			0.490414	+	0.871490i	$0.336846\pi$
$500$	−2.31218e14	+	3.83792e14i	−0.330892	+	0.549239i
$501$		0			0
$502$			4.45934e13i			0.0624310i
$503$			9.66327e14i			1.33814i	0.743202	+	0.669068i	$0.233306\pi$
$503$			9.66327e14i			1.33814i	−0.743202	+	0.669068i	$0.766694\pi$
$504$		0			0
$505$	−2.06836e14	+	7.38311e13i	−0.280235	+	0.100032i
$506$	−7.62893e13			−0.102243
$507$		0			0
$508$		−	2.99796e11i		−	0.000393166i
$509$	1.19572e13			0.0155125			0.00775626	−	0.999970i	$-0.497531\pi$
$509$	1.19572e13			0.0155125			0.00775626	+	0.999970i	$0.497531\pi$
$510$		0			0
$511$	−1.28212e15			−1.62785
$512$			8.32750e13i			0.104600i
$513$		0			0
$514$	−8.56614e14			−1.05314
$515$	8.04760e13	+	2.25451e14i	0.0978874	+	0.274229i
$516$		0			0
$517$			1.75695e14i			0.209199i
$518$		−	9.79321e11i		−	0.00115375i
$519$		0			0
$520$	−6.76070e14	+	2.41327e14i	−0.779782	+	0.278347i
$521$	−1.26458e15			−1.44324			−0.721618	−	0.692292i	$-0.756601\pi$
$521$	−1.26458e15			−1.44324			−0.721618	+	0.692292i	$0.756601\pi$
$522$		0			0
$523$		−	7.08792e13i		−	0.0792062i	−0.999215	−	0.0396031i	$-0.987391\pi$
$523$		−	7.08792e13i		−	0.0792062i	0.999215	−	0.0396031i	$-0.0126094\pi$
$524$	6.86820e14			0.759487
$525$		0			0
$526$	−4.07807e13			−0.0441605
$527$		−	1.58312e15i		−	1.69650i
$528$		0			0
$529$	8.96321e14			0.940713
$530$	−6.82336e14	+	2.43563e14i	−0.708730	+	0.252985i
$531$		0			0
$532$		−	5.27611e14i		−	0.536784i
$533$			9.25643e14i			0.932060i
$534$		0			0
$535$	−4.95391e14	−	1.38782e15i	−0.488655	−	1.36895i
$536$	−1.92560e14			−0.188001
$537$		0			0
$538$		−	1.05898e15i		−	1.01295i
$539$	−9.19966e14			−0.871031
$540$		0			0
$541$	1.90242e15			1.76491			0.882453	−	0.470400i	$-0.155890\pi$
$541$	1.90242e15			1.76491			0.882453	+	0.470400i	$0.155890\pi$
$542$		−	1.23264e14i		−	0.113198i
$543$		0			0
$544$	−1.12238e15			−1.01005
$545$	9.53970e13	−	3.40525e13i	0.0849873	−	0.0303367i
$546$		0			0
$547$			1.94867e13i			0.0170141i	0.999964	+	0.00850704i	$0.00270791\pi$
$547$			1.94867e13i			0.0170141i	−0.999964	+	0.00850704i	$0.997292\pi$
$548$		−	2.68323e14i		−	0.231934i
$549$		0			0
$550$	3.13841e14	+	3.83595e14i	0.265898	+	0.324996i
$551$	2.93860e14			0.246494
$552$		0			0
$553$			3.02888e15i			2.49054i
$554$	6.01910e14			0.490036
$555$		0			0
$556$	1.44822e14			0.115591
$557$			1.67247e15i			1.32177i	0.750489	+	0.660883i	$0.229818\pi$
$557$			1.67247e15i			1.32177i	−0.750489	+	0.660883i	$0.770182\pi$
$558$		0			0
$559$	−6.80450e14			−0.527268
$560$	−3.43569e13	−	9.62499e13i	−0.0263621	−	0.0738527i
$561$		0			0
$562$			6.14544e14i			0.462384i
$563$			7.96866e13i			0.0593730i	0.999559	+	0.0296865i	$0.00945090\pi$
$563$			7.96866e13i			0.0593730i	−0.999559	+	0.0296865i	$0.990549\pi$
$564$		0			0
$565$	5.04166e12	+	1.41241e13i	0.00368390	+	0.0103203i
$566$	7.97653e14			0.577196
$567$		0			0
$568$			4.43702e14i			0.314902i
$569$	2.11263e15			1.48493			0.742467	−	0.669883i	$-0.233656\pi$
$569$	2.11263e15			1.48493			0.742467	+	0.669883i	$0.233656\pi$
$570$		0			0
$571$	1.05231e15			0.725513			0.362756	−	0.931884i	$-0.381836\pi$
$571$	1.05231e15			0.725513			0.362756	+	0.931884i	$0.381836\pi$
$572$		−	5.54432e14i		−	0.378591i
$573$		0			0
$574$	1.48188e15			0.992653
$575$	2.32387e14	+	2.84037e14i	0.154184	+	0.188452i
$576$		0			0
$577$			1.13168e15i			0.736642i	0.929699	+	0.368321i	$0.120067\pi$
$577$			1.13168e15i			0.736642i	−0.929699	+	0.368321i	$0.879933\pi$
$578$			8.00698e12i			0.00516257i
$579$		0			0
$580$	4.20909e14	−	1.50246e14i	0.266277	−	0.0950491i
$581$	2.40701e15			1.50838
$582$		0			0
$583$		−	1.43225e15i		−	0.880727i
$584$	−1.75430e15			−1.06864
$585$		0			0
$586$	−1.09010e15			−0.651675
$587$		−	8.84276e14i		−	0.523695i	−0.965109	−	0.261847i	$-0.915668\pi$
$587$		−	8.84276e14i		−	0.523695i	0.965109	−	0.261847i	$-0.0843317\pi$
$588$		0			0
$589$	1.63870e15			0.952503
$590$	1.39898e14	+	3.91921e14i	0.0805612	+	0.225690i
$591$		0			0
$592$			1.19162e11i			6.73548e-5i
$593$		−	2.89873e15i		−	1.62333i	−0.584123	−	0.811665i	$-0.698562\pi$
$593$		−	2.89873e15i		−	1.62333i	0.584123	−	0.811665i	$-0.301438\pi$
$594$		0			0
$595$	2.55439e15	−	9.11804e14i	1.40425	−	0.501254i
$596$	−6.71134e14			−0.365557
$597$		0			0
$598$			2.29714e14i			0.122837i
$599$	−2.28284e15			−1.20956			−0.604781	−	0.796392i	$-0.706739\pi$
$599$	−2.28284e15			−1.20956			−0.604781	+	0.796392i	$0.706739\pi$
$600$		0			0
$601$	1.28437e15			0.668159			0.334080	−	0.942545i	$-0.391575\pi$
$601$	1.28437e15			0.668159			0.334080	+	0.942545i	$0.391575\pi$
$602$			1.08935e15i			0.561545i
$603$		0			0
$604$	−4.28942e13			−0.0217118
$605$	9.54885e14	−	3.40851e14i	0.478957	−	0.170966i
$606$		0			0
$607$			5.70541e14i			0.281027i	0.990079	+	0.140514i	$0.0448754\pi$
$607$			5.70541e14i			0.281027i	−0.990079	+	0.140514i	$0.955125\pi$
$608$		−	1.16178e15i		−	0.567095i
$609$		0			0
$610$	4.63689e14	+	1.29901e15i	0.222286	+	0.622728i
$611$	5.29032e14			0.251336
$612$		0			0
$613$		−	3.14628e15i		−	1.46813i	−0.679080	−	0.734065i	$-0.737621\pi$
$613$		−	3.14628e15i		−	1.46813i	0.679080	−	0.734065i	$-0.262379\pi$
$614$	−3.18690e14			−0.147381
$615$		0			0
$616$	−2.27186e15			−1.03202
$617$			3.60874e15i			1.62475i	0.583135	+	0.812375i	$0.301826\pi$
$617$			3.60874e15i			1.62475i	−0.583135	+	0.812375i	$0.698174\pi$
$618$		0			0
$619$	−2.19239e15			−0.969660			−0.484830	−	0.874608i	$-0.661118\pi$
$619$	−2.19239e15			−0.969660			−0.484830	+	0.874608i	$0.661118\pi$
$620$	2.34719e15	−	8.37843e14i	1.02895	−	0.367289i
$621$		0			0
$622$		−	2.62096e14i		−	0.112879i
$623$			2.28957e14i			0.0977394i
$624$		0			0
$625$	4.72182e14	−	2.33696e15i	0.198048	−	0.980192i
$626$	−2.15756e15			−0.897024
$627$		0			0
$628$			1.70210e15i			0.695357i
$629$	−3.16246e12			−0.00128070
$630$		0			0
$631$	3.99257e14			0.158888			0.0794441	−	0.996839i	$-0.474685\pi$
$631$	3.99257e14			0.158888			0.0794441	+	0.996839i	$0.474685\pi$
$632$			4.14433e15i			1.63497i
$633$		0			0
$634$	−8.16291e14			−0.316486
$635$	5.36292e11	+	1.50241e12i	0.000206132	+	0.000577473i
$636$		0			0
$637$			2.77010e15i			1.04647i
$638$		−	4.94361e14i		−	0.185153i
$639$		0			0
$640$	−6.22644e14	−	1.74432e15i	−0.229219	−	0.642149i
$641$	1.23875e15			0.452132			0.226066	−	0.974112i	$-0.427414\pi$
$641$	1.23875e15			0.452132			0.226066	+	0.974112i	$0.427414\pi$
$642$		0			0
$643$			2.78159e15i			0.998005i	0.866601	+	0.499003i	$0.166300\pi$
$643$			2.78159e15i			0.998005i	−0.866601	+	0.499003i	$0.833700\pi$
$644$	−6.57234e14			−0.233802
$645$		0			0
$646$	9.53345e14			0.333404
$647$		−	3.99567e15i		−	1.38553i	−0.721163	−	0.692766i	$-0.756392\pi$
$647$		−	3.99567e15i		−	1.38553i	0.721163	−	0.692766i	$-0.243608\pi$
$648$		0			0
$649$	−8.22656e14			−0.280461
$650$	1.15504e15	−	9.45003e14i	0.390456	−	0.319455i
$651$		0			0
$652$		−	1.25212e15i		−	0.416182i
$653$			1.37144e15i			0.452016i	0.974125	+	0.226008i	$0.0725675\pi$
$653$			1.37144e15i			0.452016i	−0.974125	+	0.226008i	$0.927432\pi$
$654$		0			0
$655$	−3.44194e15	+	1.22862e15i	−1.11552	+	0.398190i
$656$	−1.80312e14			−0.0579502
$657$		0			0
$658$		−	8.46936e14i		−	0.267675i
$659$	−4.53043e15			−1.41994			−0.709969	−	0.704233i	$-0.751291\pi$
$659$	−4.53043e15			−1.41994			−0.709969	+	0.704233i	$0.751291\pi$
$660$		0			0
$661$	−8.53788e13			−0.0263174			−0.0131587	−	0.999913i	$-0.504189\pi$
$661$	−8.53788e13			−0.0263174			−0.0131587	+	0.999913i	$0.504189\pi$
$662$		−	2.46529e15i		−	0.753613i
$663$		0			0
$664$	3.29345e15			0.990209
$665$	9.43819e14	+	2.64408e15i	0.281430	+	0.788417i
$666$		0			0
$667$		−	3.66055e14i		−	0.107363i
$668$			2.84243e15i			0.826836i
$669$		0			0
$670$	3.77021e14	−	1.34580e14i	0.107883	−	0.0385095i
$671$	−2.72667e15			−0.773854
$672$		0			0
$673$			2.76196e13i			0.00771143i	0.999993	+	0.00385571i	$0.00122732\pi$
$673$			2.76196e13i			0.00771143i	−0.999993	+	0.00385571i	$0.998773\pi$
$674$	−1.82038e15			−0.504119
$675$		0			0
$676$	6.84025e14			0.186365
$677$		−	5.40053e15i		−	1.45948i	−0.683724	−	0.729741i	$-0.739641\pi$
$677$		−	5.40053e15i		−	1.45948i	0.683724	−	0.729741i	$-0.260359\pi$
$678$		0			0
$679$	−1.04891e16			−2.78903
$680$	3.49511e15	−	1.24760e15i	0.921853	−	0.329060i
$681$		0			0
$682$		−	2.75680e15i		−	0.715469i
$683$			1.45094e15i			0.373539i	0.982404	+	0.186769i	$0.0598017\pi$
$683$			1.45094e15i			0.373539i	−0.982404	+	0.186769i	$0.940198\pi$
$684$		0			0
$685$	4.79991e14	+	1.34468e15i	0.121600	+	0.340660i
$686$	8.65527e14			0.217519
$687$		0			0
$688$		−	1.32550e14i		−	0.0327825i
$689$	−4.31263e15			−1.05812
$690$		0			0
$691$	−3.79473e15			−0.916330			−0.458165	−	0.888867i	$-0.651493\pi$
$691$	−3.79473e15			−0.916330			−0.458165	+	0.888867i	$0.651493\pi$
$692$		−	4.93826e14i		−	0.118302i
$693$		0			0
$694$	−2.71553e15			−0.640291
$695$	−7.25766e14	+	2.59066e14i	−0.169778	+	0.0606030i
$696$		0			0
$697$		−	4.78534e15i		−	1.10188i
$698$		−	9.68636e13i		−	0.0221287i
$699$		0			0
$700$	2.70375e15	+	3.30468e15i	0.608033	+	0.743173i
$701$	3.00014e15			0.669410			0.334705	−	0.942323i	$-0.391363\pi$
$701$	3.00014e15			0.669410			0.334705	+	0.942323i	$0.391363\pi$
$702$		0			0
$703$		−	3.27350e12i		−	0.000719048i
$704$	−1.78604e15			−0.389261
$705$		0			0
$706$	1.15759e15			0.248387
$707$			2.09285e15i			0.445586i
$708$		0			0
$709$	3.33135e14			0.0698338			0.0349169	−	0.999390i	$-0.488883\pi$
$709$	3.33135e14			0.0698338			0.0349169	+	0.999390i	$0.488883\pi$
$710$	−3.10101e14	−	8.68739e14i	−0.0645033	−	0.180704i
$711$		0			0
$712$			3.13276e14i			0.0641634i
$713$		−	2.04130e15i		−	0.414872i
$714$		0			0
$715$	9.91799e14	+	2.77850e15i	0.198491	+	0.556066i
$716$	1.31043e15			0.260250
$717$		0			0
$718$		−	3.65645e15i		−	0.715114i
$719$	1.88706e15			0.366249			0.183124	−	0.983090i	$-0.441379\pi$
$719$	1.88706e15			0.366249			0.183124	+	0.983090i	$0.441379\pi$
$720$		0			0
$721$	2.28121e15			0.436035
$722$		−	2.17090e15i		−	0.411799i
$723$		0			0
$724$	4.36970e15			0.816374
$725$	−1.84058e15	+	1.50589e15i	−0.341269	+	0.279212i
$726$		0			0
$727$		−	3.20690e15i		−	0.585660i	−0.956164	−	0.292830i	$-0.905403\pi$
$727$		−	3.20690e15i		−	0.585660i	0.956164	−	0.292830i	$-0.0945970\pi$
$728$			6.84076e15i			1.23989i
$729$		0			0
$730$	3.43480e15	−	1.22607e15i	0.613233	−	0.218897i
$731$	3.51776e15			0.623333
$732$		0			0
$733$		−	4.94602e15i		−	0.863344i	−0.902031	−	0.431672i	$-0.857924\pi$
$733$		−	4.94602e15i		−	0.863344i	0.902031	−	0.431672i	$-0.142076\pi$
$734$	2.83339e15			0.490883
$735$		0			0
$736$	−1.44721e15			−0.247004
$737$			7.91381e14i			0.134065i
$738$		0			0
$739$	−2.24992e15			−0.375511			−0.187756	−	0.982216i	$-0.560121\pi$
$739$	−2.24992e15			−0.375511			−0.187756	+	0.982216i	$0.560121\pi$
$740$	−1.67369e12	−	4.68878e12i	−0.000277268	−	0.000776758i
$741$		0			0
$742$			6.90416e15i			1.12691i
$743$		−	6.59378e15i		−	1.06831i	−0.845387	−	0.534154i	$-0.820630\pi$
$743$		−	6.59378e15i		−	1.06831i	0.845387	−	0.534154i	$-0.179370\pi$
$744$		0			0
$745$	3.36333e15	−	1.20056e15i	0.536921	−	0.191657i
$746$	6.58200e15			1.04302
$747$		0			0
$748$			2.86628e15i			0.447568i
$749$	−1.40426e16			−2.17669
$750$		0			0
$751$	4.76790e15			0.728295			0.364147	−	0.931341i	$-0.381360\pi$
$751$	4.76790e15			0.728295			0.364147	+	0.931341i	$0.381360\pi$
$752$			1.03054e14i			0.0156266i
$753$		0			0
$754$	−1.48856e15			−0.222446
$755$	2.14961e14	−	7.67315e13i	0.0318898	−	0.0113832i
$756$		0			0
$757$			3.60332e15i			0.526836i	0.964682	+	0.263418i	$0.0848499\pi$
$757$			3.60332e15i			0.526836i	−0.964682	+	0.263418i	$0.915150\pi$
$758$		−	3.80820e15i		−	0.552763i
$759$		0			0
$760$	1.29140e15	+	3.61783e15i	0.184751	+	0.517575i
$761$	1.00138e16			1.42227			0.711136	−	0.703054i	$-0.248181\pi$
$761$	1.00138e16			1.42227			0.711136	+	0.703054i	$0.248181\pi$
$762$		0			0
$763$		−	9.65267e14i		−	0.135133i
$764$	5.29031e15			0.735306
$765$		0			0
$766$	5.88702e15			0.806561
$767$			2.47709e15i			0.336951i
$768$		0			0
$769$	1.14898e16			1.54070			0.770351	−	0.637620i	$-0.220081\pi$
$769$	1.14898e16			1.54070			0.770351	+	0.637620i	$0.220081\pi$
$770$	4.44814e15	−	1.58779e15i	0.592216	−	0.211395i
$771$		0			0
$772$			1.33760e15i			0.175562i
$773$			1.24078e16i			1.61699i	0.588501	+	0.808497i	$0.299718\pi$
$773$			1.24078e16i			1.61699i	−0.588501	+	0.808497i	$0.700282\pi$
$774$		0			0
$775$	−1.02640e16	+	8.39757e15i	−1.31873	+	1.07893i
$776$	−1.43519e16			−1.83092
$777$		0			0
$778$			6.18192e15i			0.777562i
$779$	4.95336e15			0.618649
$780$		0			0
$781$	1.82352e15			0.224558
$782$		−	1.18756e15i		−	0.145217i
$783$		0			0
$784$	−5.39607e14			−0.0650637
$785$	−3.04482e15	−	8.52996e15i	−0.364568	−	1.02133i
$786$		0			0
$787$		−	3.57890e15i		−	0.422560i	−0.977426	−	0.211280i	$-0.932237\pi$
$787$		−	3.57890e15i		−	0.422560i	0.977426	−	0.211280i	$-0.0677631\pi$
$788$		−	5.99805e15i		−	0.703260i
$789$		0			0
$790$	−2.89645e15	−	8.11433e15i	−0.334902	−	0.938217i
$791$	1.42913e14			0.0164098
$792$		0			0
$793$			8.21024e15i			0.929723i
$794$	2.08308e15			0.234258
$795$		0			0
$796$	2.88737e15			0.320244
$797$			1.25596e16i			1.38343i	0.722172	+	0.691714i	$0.243144\pi$
$797$			1.25596e16i			1.38343i	−0.722172	+	0.691714i	$0.756856\pi$
$798$		0			0
$799$	−2.73496e15			−0.297128
$800$	5.95358e15	+	7.27681e15i	0.642367	+	0.785138i
$801$		0			0
$802$		−	7.96160e15i		−	0.847308i
$803$			7.20977e15i			0.762055i
$804$		0			0
$805$	3.29368e15	−	1.17570e15i	0.343403	−	0.122579i
$806$	−8.30095e15			−0.859578
$807$		0			0
$808$			2.86359e15i			0.292515i
$809$	8.95686e15			0.908738			0.454369	−	0.890813i	$-0.349865\pi$
$809$	8.95686e15			0.908738			0.454369	+	0.890813i	$0.349865\pi$
$810$		0			0
$811$	−8.33940e15			−0.834680			−0.417340	−	0.908750i	$-0.637038\pi$
$811$	−8.33940e15			−0.834680			−0.417340	+	0.908750i	$0.637038\pi$
$812$		−	4.25893e15i		−	0.423392i
$813$		0			0
$814$	−5.50702e12			−0.000540110
$815$	2.23985e15	+	6.27489e15i	0.218199	+	0.611278i
$816$		0			0
$817$			3.64127e15i			0.349971i
$818$		−	3.57545e15i		−	0.341340i
$819$		0			0
$820$	7.09493e15	−	2.53257e15i	0.668300	−	0.238553i
$821$	−3.07549e15			−0.287757			−0.143879	−	0.989595i	$-0.545958\pi$
$821$	−3.07549e15			−0.287757			−0.143879	+	0.989595i	$0.545958\pi$
$822$		0			0
$823$		−	1.67606e16i		−	1.54736i	−0.633579	−	0.773678i	$-0.718415\pi$
$823$		−	1.67606e16i		−	1.54736i	0.633579	−	0.773678i	$-0.281585\pi$
$824$	3.12132e15			0.286246
$825$		0			0
$826$	3.96562e15			0.358856
$827$		−	1.18413e16i		−	1.06443i	−0.846608	−	0.532217i	$-0.821359\pi$
$827$		−	1.18413e16i		−	1.06443i	0.846608	−	0.532217i	$-0.178641\pi$
$828$		0			0
$829$	3.10234e15			0.275195			0.137597	−	0.990488i	$-0.456062\pi$
$829$	3.10234e15			0.275195			0.137597	+	0.990488i	$0.456062\pi$
$830$	−6.44836e15	+	2.30178e15i	−0.568225	+	0.202831i
$831$		0			0
$832$			5.37792e15i			0.467666i
$833$		−	1.43207e16i		−	1.23713i
$834$		0			0
$835$	−5.08470e15	−	1.42446e16i	−0.433500	−	1.21444i
$836$	−2.96691e15			−0.251287
$837$		0			0
$838$			9.43094e15i			0.788339i
$839$	−2.08909e16			−1.73487			−0.867436	−	0.497549i	$-0.834233\pi$
$839$	−2.08909e16			−1.73487			−0.867436	+	0.497549i	$0.834233\pi$
$840$		0			0
$841$	−9.82844e15			−0.805576
$842$			9.75908e15i			0.794680i
$843$		0			0
$844$	1.10239e15			0.0886039
$845$	−3.42794e15	+	1.22362e15i	−0.273729	+	0.0977091i
$846$		0			0
$847$		−	9.66193e15i		−	0.761562i
$848$		−	8.40086e14i		−	0.0657880i
$849$		0			0
$850$	−5.97125e15	+	4.88543e15i	−0.461595	+	0.377658i
$851$	−4.07773e12			−0.000313189
$852$		0			0
$853$			2.42451e16i			1.83825i	0.393968	+	0.919124i	$0.371102\pi$
$853$			2.42451e16i			1.83825i	−0.393968	+	0.919124i	$0.628898\pi$
$854$	1.31439e16			0.990164
$855$		0			0
$856$	−1.92141e16			−1.42894
$857$		−	9.53835e15i		−	0.704821i	−0.935846	−	0.352410i	$-0.885362\pi$
$857$		−	9.53835e15i		−	0.704821i	0.935846	−	0.352410i	$-0.114638\pi$
$858$		0			0
$859$	−4.70173e15			−0.343001			−0.171500	−	0.985184i	$-0.554861\pi$
$859$	−4.70173e15			−0.343001			−0.171500	+	0.985184i	$0.554861\pi$
$860$	1.86172e15	+	5.21556e15i	0.134950	+	0.378059i
$861$		0			0
$862$		−	1.09254e16i		−	0.781893i
$863$		−	1.12556e16i		−	0.800401i	−0.916428	−	0.400201i	$-0.868940\pi$
$863$		−	1.12556e16i		−	0.800401i	0.916428	−	0.400201i	$-0.131060\pi$
$864$		0			0
$865$	8.83383e14	+	2.47477e15i	0.0620241	+	0.173759i
$866$	−1.02855e16			−0.717593
$867$		0			0
$868$		−	2.37499e16i		−	1.63607i
$869$	1.70323e16			1.16591
$870$		0			0
$871$	2.38292e15			0.161068
$872$		−	1.32075e15i		−	0.0887115i
$873$		0			0
$874$	1.22926e15			0.0815324
$875$	−1.94612e16	−	1.17245e16i	−1.28270	−	0.772771i
$876$		0			0
$877$		−	9.19338e15i		−	0.598381i	−0.954193	−	0.299190i	$-0.903283\pi$
$877$		−	9.19338e15i		−	0.598381i	0.954193	−	0.299190i	$-0.0967165\pi$
$878$			1.54515e16i			0.999424i
$879$		0			0
$880$	−5.41242e14	+	1.93199e14i	−0.0345730	+	0.0123410i
$881$	1.98624e16			1.26085			0.630425	−	0.776250i	$-0.282880\pi$
$881$	1.98624e16			1.26085			0.630425	+	0.776250i	$0.282880\pi$
$882$		0			0
$883$		−	5.79702e15i		−	0.363430i	−0.983351	−	0.181715i	$-0.941835\pi$
$883$		−	5.79702e15i		−	0.363430i	0.983351	−	0.181715i	$-0.0581648\pi$
$884$	8.63061e15			0.537717
$885$		0			0
$886$	−1.77468e16			−1.09203
$887$		−	8.29351e15i		−	0.507176i	−0.967312	−	0.253588i	$-0.918389\pi$
$887$		−	8.29351e15i		−	0.507176i	0.967312	−	0.253588i	$-0.0816107\pi$
$888$		0			0
$889$	1.52020e13			0.000918206
$890$	−2.18947e14	−	6.13374e14i	−0.0131430	−	0.0368197i
$891$		0			0
$892$			2.12684e16i			1.26104i
$893$		−	2.83099e15i		−	0.166823i
$894$		0			0
$895$	−6.56710e15	+	2.34416e15i	−0.382249	+	0.136446i
$896$	−1.76498e16			−1.02104
$897$		0			0
$898$			5.87525e15i			0.335742i
$899$	1.32278e16			0.751293
$900$		0			0
$901$	2.22952e16			1.25091
$902$		−	8.33305e15i		−	0.464695i
$903$		0			0
$904$	1.95545e14			0.0107726
$905$	−2.18984e16	+	7.81675e15i	−1.19907	+	0.428015i
$906$		0			0
$907$			2.89763e16i			1.56748i	0.621088	+	0.783741i	$0.286691\pi$
$907$			2.89763e16i			1.56748i	−0.621088	+	0.783741i	$0.713309\pi$
$908$		−	7.99059e14i		−	0.0429642i
$909$		0			0
$910$	−4.78097e15	−	1.33938e16i	−0.253974	−	0.711499i
$911$	−1.91910e16			−1.01332			−0.506659	−	0.862147i	$-0.669120\pi$
$911$	−1.91910e16			−1.01332			−0.506659	+	0.862147i	$0.669120\pi$
$912$		0			0
$913$		−	1.35354e16i		−	0.706123i
$914$	−1.09737e16			−0.569046
$915$		0			0
$916$	−2.09770e16			−1.07478
$917$			3.48270e16i			1.77372i
$918$		0			0
$919$	5.30946e15			0.267187			0.133593	−	0.991036i	$-0.457348\pi$
$919$	5.30946e15			0.267187			0.133593	+	0.991036i	$0.457348\pi$
$920$	4.50665e15	−	1.60867e15i	0.225435	−	0.0804702i
$921$		0			0
$922$			1.29589e16i			0.640542i
$923$		−	5.49076e15i		−	0.269788i
$924$		0			0
$925$	1.67751e13	+	2.05035e13i	0.000814489	+	0.000995516i
$926$	−2.14379e15			−0.103472
$927$		0			0
$928$		−	9.37804e15i		−	0.447299i
$929$	3.41655e16			1.61995			0.809974	−	0.586466i	$-0.199481\pi$
$929$	3.41655e16			1.61995			0.809974	+	0.586466i	$0.199481\pi$
$930$		0			0
$931$	1.48235e16			0.694590
$932$			1.43792e16i			0.669805i
$933$		0			0
$934$	1.04088e16			0.479174
$935$	−5.12735e15	−	1.43641e16i	−0.234655	−	0.657378i
$936$		0			0
$937$			1.15303e16i			0.521524i	0.965403	+	0.260762i	$0.0839738\pi$
$937$			1.15303e16i			0.521524i	−0.965403	+	0.260762i	$0.916026\pi$
$938$		−	3.81485e15i		−	0.171539i
$939$		0			0
$940$	−1.44744e15	−	4.05495e15i	−0.0643275	−	0.180212i
$941$	3.10666e16			1.37262			0.686310	−	0.727309i	$-0.259229\pi$
$941$	3.10666e16			1.37262			0.686310	+	0.727309i	$0.259229\pi$
$942$		0			0
$943$		−	6.17030e15i		−	0.269459i
$944$	−4.82529e14			−0.0209497
$945$		0			0
$946$	6.12572e15			0.262879
$947$			3.79319e16i			1.61838i	0.587550	+	0.809188i	$0.300092\pi$
$947$			3.79319e16i			1.61838i	−0.587550	+	0.809188i	$0.699908\pi$
$948$		0			0
$949$	2.17093e16			0.915547
$950$	−5.05696e15	−	6.18091e15i	−0.212036	−	0.259163i
$951$		0			0
$952$		−	3.53650e16i		−	1.46578i
$953$			1.52578e16i			0.628756i	0.949298	+	0.314378i	$0.101796\pi$
$953$			1.52578e16i			0.628756i	−0.949298	+	0.314378i	$0.898204\pi$
$954$		0			0
$955$	−2.65120e16	+	9.46360e15i	−1.08000	+	0.385512i
$956$	−2.77785e16			−1.12510
$957$		0			0
$958$			1.17645e16i			0.471045i
$959$	1.36060e16			0.541663
$960$		0			0
$961$	4.83561e16			1.90315
$962$			1.65821e13i			0.000648898i
$963$		0			0
$964$	1.85776e16			0.718731
$965$	−2.39277e15	−	6.70328e15i	−0.0920452	−	0.257862i
$966$		0			0
$967$			8.70387e15i			0.331029i	0.986207	+	0.165515i	$0.0529285\pi$
$967$			8.70387e15i			0.331029i	−0.986207	+	0.165515i	$0.947071\pi$
$968$		−	1.32202e16i		−	0.499945i
$969$		0			0
$970$	2.81001e16	−	1.00305e16i	1.05066	−	0.375039i
$971$	6.67861e15			0.248302			0.124151	−	0.992263i	$-0.460379\pi$
$971$	6.67861e15			0.248302			0.124151	+	0.992263i	$0.460379\pi$
$972$		0			0
$973$			7.34361e15i			0.269953i
$974$	9.10715e15			0.332896
$975$		0			0
$976$	−1.59933e15			−0.0578048
$977$		−	3.64352e16i		−	1.30949i	−0.755851	−	0.654744i	$-0.772777\pi$
$977$		−	3.64352e16i		−	1.30949i	0.755851	−	0.654744i	$-0.227223\pi$
$978$		0			0
$979$	1.28749e15			0.0457552
$980$	2.12324e16	−	7.57903e15i	0.750336	−	0.267837i
$981$		0			0
$982$			1.74587e16i			0.610097i
$983$			3.91117e16i			1.35913i	0.733613	+	0.679567i	$0.237832\pi$
$983$			3.91117e16i			1.35913i	−0.733613	+	0.679567i	$0.762168\pi$
$984$		0			0
$985$	1.07296e16	+	3.00588e16i	0.368711	+	1.03293i
$986$	7.69550e15			0.262975
$987$		0			0
$988$			8.93364e15i			0.301901i
$989$	4.53585e15			0.152433
$990$		0			0
$991$	−3.51778e15			−0.116913			−0.0584566	−	0.998290i	$-0.518618\pi$
$991$	−3.51778e15			−0.116913			−0.0584566	+	0.998290i	$0.518618\pi$
$992$		−	5.22965e16i		−	1.72846i
$993$		0			0
$994$	−8.79026e15			−0.287327
$995$	−1.44698e16	+	5.16508e15i	−0.470366	+	0.167900i
$996$		0			0
$997$			2.71445e15i			0.0872687i	0.999048	+	0.0436343i	$0.0138937\pi$
$997$			2.71445e15i			0.0872687i	−0.999048	+	0.0436343i	$0.986106\pi$
$998$			1.83751e16i			0.587505i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.12.b.b.19.3		4
3.2	odd	2		5.12.b.a.4.2	✓	4
5.2	odd	4		225.12.a.r.1.2		4
5.3	odd	4		225.12.a.r.1.3		4
5.4	even	2	inner	45.12.b.b.19.2		4
12.11	even	2		80.12.c.a.49.1		4
15.2	even	4		25.12.a.e.1.3		4
15.8	even	4		25.12.a.e.1.2		4
15.14	odd	2		5.12.b.a.4.3	yes	4
60.59	even	2		80.12.c.a.49.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.12.b.a.4.2	✓	4	3.2	odd	2
5.12.b.a.4.3	yes	4	15.14	odd	2
25.12.a.e.1.2		4	15.8	even	4
25.12.a.e.1.3		4	15.2	even	4
45.12.b.b.19.2		4	5.4	even	2	inner
45.12.b.b.19.3		4	1.1	even	1	trivial
80.12.c.a.49.1		4	12.11	even	2
80.12.c.a.49.4		4	60.59	even	2
225.12.a.r.1.2		4	5.2	odd	4
225.12.a.r.1.3		4	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+27.1071i q^{2} +1313.20 q^{4} +(-6581.01 + 2349.13i) q^{5} +66589.5i q^{7} +91112.6i q^{8} +O(q^{10})\)	\(q+27.1071i q^{2} +1313.20 q^{4} +(-6581.01 + 2349.13i) q^{5} +66589.5i q^{7} +91112.6i q^{8} +(-63678.2 - 178392. i) q^{10} +374453. q^{11} -1.12751e6i q^{13} -1.80505e6 q^{14} +219635. q^{16} +5.82894e6i q^{17} -6.03360e6 q^{19} +(-8.64220e6 + 3.08488e6i) q^{20} +1.01503e7i q^{22} +7.51593e6i q^{23} +(3.77913e7 - 3.09193e7i) q^{25} +3.05636e7 q^{26} +8.74454e7i q^{28} -4.87039e7 q^{29} -2.71596e8 q^{31} +1.92552e8i q^{32} -1.58006e8 q^{34} +(-1.56427e8 - 4.38226e8i) q^{35} +542545. i q^{37} -1.63554e8i q^{38} +(-2.14035e8 - 5.99613e8i) q^{40} -8.20963e8 q^{41} -6.03499e8i q^{43} +4.91732e8 q^{44} -2.03735e8 q^{46} +4.69204e8i q^{47} -2.45683e9 q^{49} +(8.38134e8 + 1.02441e9i) q^{50} -1.48065e9i q^{52} -3.82491e9i q^{53} +(-2.46428e9 + 8.79637e8i) q^{55} -6.06714e9 q^{56} -1.32022e9i q^{58} -2.19696e9 q^{59} -7.28175e9 q^{61} -7.36220e9i q^{62} -4.76973e9 q^{64} +(2.64866e9 + 7.42015e9i) q^{65} +2.11343e9i q^{67} +7.65458e9i q^{68} +(1.18791e10 - 4.24029e9i) q^{70} +4.86982e9 q^{71} +1.92542e10i q^{73} -1.47068e7 q^{74} -7.92334e9 q^{76} +2.49346e10i q^{77} +4.54858e10 q^{79} +(-1.44542e9 + 5.15952e8i) q^{80} -2.22540e10i q^{82} -3.61471e10i q^{83} +(-1.36929e10 - 3.83603e10i) q^{85} +1.63591e10 q^{86} +3.41174e10i q^{88} +3.43834e9 q^{89} +7.50802e10 q^{91} +9.86994e9i q^{92} -1.27188e10 q^{94} +(3.97072e10 - 1.41737e10i) q^{95} +1.57518e11i q^{97} -6.65976e10i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 72 q^{4} + 300 q^{5}+O(q^{10}) \) 4 * q - 72 * q^4 + 300 * q^5	\( 4 q - 72 q^{4} + 300 q^{5} + 91400 q^{10} + 326352 q^{11} - 1080696 q^{14} - 9834976 q^{16} + 15460880 q^{19} - 35447400 q^{20} + 159152500 q^{25} + 325970832 q^{26} - 216242520 q^{29} - 684043072 q^{31} + 265782016 q^{34} - 394292400 q^{35} - 275204000 q^{40} - 1012873368 q^{41} + 1553573664 q^{44} + 5241789688 q^{46} - 1900646372 q^{49} + 4621170000 q^{50} - 7772763600 q^{55} - 10366738080 q^{56} - 3200971440 q^{59} - 2310471352 q^{61} - 5401150592 q^{64} - 3229723200 q^{65} + 40783573800 q^{70} + 60335466912 q^{71} + 5525992944 q^{74} - 52987638240 q^{76} + 74637768320 q^{79} - 72046927200 q^{80} - 46117585600 q^{85} - 39045421128 q^{86} - 118272499560 q^{89} + 51565095648 q^{91} - 266098749224 q^{94} + 264706278000 q^{95}+O(q^{100}) \) 4 * q - 72 * q^4 + 300 * q^5 + 91400 * q^10 + 326352 * q^11 - 1080696 * q^14 - 9834976 * q^16 + 15460880 * q^19 - 35447400 * q^20 + 159152500 * q^25 + 325970832 * q^26 - 216242520 * q^29 - 684043072 * q^31 + 265782016 * q^34 - 394292400 * q^35 - 275204000 * q^40 - 1012873368 * q^41 + 1553573664 * q^44 + 5241789688 * q^46 - 1900646372 * q^49 + 4621170000 * q^50 - 7772763600 * q^55 - 10366738080 * q^56 - 3200971440 * q^59 - 2310471352 * q^61 - 5401150592 * q^64 - 3229723200 * q^65 + 40783573800 * q^70 + 60335466912 * q^71 + 5525992944 * q^74 - 52987638240 * q^76 + 74637768320 * q^79 - 72046927200 * q^80 - 46117585600 * q^85 - 39045421128 * q^86 - 118272499560 * q^89 + 51565095648 * q^91 - 266098749224 * q^94 + 264706278000 * q^95

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